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Mirrors > Home > MPE Home > Th. List > nalset | Structured version Visualization version Unicode version |
Description: No set contains all sets. Theorem 41 of [Suppes] p. 30. (Contributed by NM, 23-Aug-1993.) |
Ref | Expression |
---|---|
nalset |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alexn 1724 |
. 2
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2 | ax-sep 4538 |
. . 3
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3 | elequ1 1904 |
. . . . . 6
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4 | elequ1 1904 |
. . . . . . 7
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5 | elequ1 1904 |
. . . . . . . . 9
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6 | elequ2 1911 |
. . . . . . . . 9
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7 | 5, 6 | bitrd 261 |
. . . . . . . 8
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8 | 7 | notbid 300 |
. . . . . . 7
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9 | 4, 8 | anbi12d 722 |
. . . . . 6
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10 | 3, 9 | bibi12d 327 |
. . . . 5
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11 | 10 | spv 2114 |
. . . 4
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12 | pclem6 946 |
. . . 4
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13 | 11, 12 | syl 17 |
. . 3
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14 | 2, 13 | eximii 1719 |
. 2
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15 | 1, 14 | mpgbi 1682 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-8 1899 ax-9 1906 ax-12 1943 ax-13 2101 ax-sep 4538 |
This theorem depends on definitions: df-bi 190 df-an 377 df-ex 1674 |
This theorem is referenced by: vprc 4554 kmlem2 8606 |
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